Learning Trajectories for Integrating K-5 Computer Science and Mathematics

Reaction to the NCTM Position Statement

July 28, 2016

NCTM has released a position statement on Computer Science and Mathematics Education, in answer to the question: “Should mathematics course requirements for high school graduation be satisfied by computer science courses?” Here’s our position on their position.

Within the statement, it becomes clear that NCTM recognizes the importance of computer science education. Indeed, this point has just been made by NCTM President Matt Larson, who notes that “Without a doubt, the addition of computer science to the school curriculum can expand students’ future opportunities,” and further that, “Without question, NCTM supports the growth of computer science education.” Yet, the position statement holds a note of caution; the main thrust is “be careful” when considering whether to count CS courses as mathematics courses. Some caution seems warranted; we do not want to deprive students of mathematics for college and career readiness by too readily replacing a math course with a computer science course. But NCTM’s statement seems to frame the issue as a zero-sum game. If computer science comes in, what goes out? What is core and what is elective in a crowded high school curriculum or a full elementary school day?

Is the zero-sum game the only way to approach adding CS education to the K-12 docket? NCTM seems to think so. Larsen says, “There is no substitute for the reasoning, sense making, and computational thinking that are learned in mathematics and later applied in computer science.” But must the addition of computer science be treated as a substitution? What if the reasoning and sense making and computational thinking can take place in mathematics – with computers at hand? That is, can we integrate or at least associate the domains so that explorations happen simultaneously?

There is reason to be optimistic that integration could happen. Programming has been integrated with geometry since the days of LOGO as just one example. (See, for example, Clements, Battista, & Sarama, 20011.) Now that computers are ubiquitous, perhaps we can grow many more examples of connections and fit them together in classroom.

Not only does integration (rather than substitution) seem possible, it could be the case that facility with computing tools and the habits of mind that students acquire programming in elementary school can help them learn mathematics. That is, perhaps the exploration of mathematics via computer science can lead to more powerful understandings than if math is addressed alone. Papert referred to this as the power principle, the idea that “using it” can come before “getting it” (Papert, 1996, p. 982), and he asserts that this is natural in most environments outside of school. And if students and teachers are using it to explore mathematics, we can hope that getting it, in both math and CS, will be facilitated.

During the LTEC project, we have been working with elementary teachers and students on explorations with computers within the context of the Everyday Mathematics (EM) curriculum. Teachers have taken EM lessons and written computing activities to accompany the concepts. Our work is just beginning, but so far we see that elementary students are very engaged when working with computer programming. We also see that teachers, when they start with the mathematics lessons, tend to have the math concepts dominate the lesson. This is not surprising; teachers, like all of us, stick close to what we are familiar with, and even the adventurous will start with what they know. But as we learn more, and as teachers do more, we may see avenues for making more seamless connections between the content areas. The NCTM Position notes that neither mathematicians nor computer scientists consider their own field to be a subfield of the other. Experts in either field, including teachers of those subjects, may therefore struggle to give the domains equal ground. In elementary school, however, teachers are often not subject specialists. Instead, they teach a multitude of subjects, making connections throughout the school day and school year. We speculate that this may work to the project’s advantage in overcoming the challenges of achieving integration with minimal loss of content.

In the corner of our eyes is an added glimmer: integration at the elementary level may be an achievable way to give early CS experiences to all students. Educators and researchers have noted the devastating repercussions when female, minority, low-income, traditionally struggling students don’t have early access to CS. Positive early experiences can allow these students to see different roads ahead that they may have not seen for themselves.

Perhaps integration without substitution is an unachievable goal. Perhaps the content areas are disconnected, or at least too disconnected in terms of what schools can do, even at the elementary level. But it seems to this project team that the effort to connect computational thinking and mathematics is a fruitful area for inquiry and exploration, and risk taking by researchers and by teachers, especially in the elementary space.

  1. Clements, D. H., Battista, M., & Sarama, J. (2001). Logo and geometry. Reston, VA: National Council of Teachers of Mathematics. 

  2. Papert, S. (1996). An exploration in the space of mathematics educations. International Journal of Computers for Mathematical Learning, 1, 95-123.